# Yet another matchstick puzzle

Inspired by this post, here there is my attempt at a matches' puzzle. The expression 1 = 850 - 9 - 6 is obviously wrong: move exactly three matches to obtain a correct expression.

Rules are:

• This is not a digital display, so digits may be built differently;
• no roman numerals are allowed;
• operators $\ne , \gt , \lt$ are not allowed;
• other operators like parentheses (two matches at a much larger angle than $\lt \gt$ ) and root (three matches) are allowed;
• there is no space for inserting digits or operators, except at the far left and far right.
• The solution is not really standard :-) – mau Mar 27 '17 at 16:50
• By correct expression you mean an equation, right? Otherwise one could simply take away the = and it would be a correct expression as there would be no mistake in it. – Zelphir Kaltstahl Mar 28 '17 at 11:30
• it would be a "well formed" expression, however – mau Mar 28 '17 at 12:57
• I assume ≥ and ≤ are also disallowed? – Please stop being evil Mar 29 '17 at 7:46
• yes, and also ~ or the likes – mau Mar 29 '17 at 8:38

Fun with negative numbers The little o acts like a point so the equation becomes $-7 = 8.0 - 9 - 6$

• I like the big decimal dot! – mau Mar 28 '17 at 13:17

My try:

"This is not a digital display, so digits may be built differently" 1=950-949
Two sticks moved from the 8 (making it 9) to form 4 using existing minis and one stick to make 9 from 6

And another one (same digits with same shape):

-1 = 960-961
One stick from 8 moved to 5 to make it 6, one stick from 1 moved to the far right to form another 1, and the minus between 9 and 6 goes to the far left to make -1.

• This is a good answer too, maybe even better than mine... the only flaw I see is that the 9s are different in shape (I don't care for the smaller 4) – mau Mar 27 '17 at 20:54
• @mau Don't complain, you said "This is not a digital display, so digits may be built differently" – mbomb007 Mar 27 '17 at 21:50
• @mau, proposed another solution with no difference between same digits, but I do not like the introduced spacing in it ;) – kamenf Mar 27 '17 at 22:39
• @mbomb007 indeed I did not complain for the 4... – mau Mar 28 '17 at 9:02
• I believe what the OP meant was that digits can be built from non-standard digital display numbers, but that digit must be built uniformly throughout the entire equation (the first 9 doesn't have the bottom part like the others). – Long Nguyen Mar 28 '17 at 19:05

Here's my solution:

Initial equation: 1 = 850 - 9 - 6
Move a matchstick from the = to the centre -: 1 - 850 = 9 - 6
Move the other matchstick from what was the = to the 6: 1 850 = 9 - 8
Finally, move the top matchstick of the 1 down to immediately below the bottom matchstick of that 1. This changes the vertical alignment of the expression: 1850 = 9 - 8
And of course, a superscript means exponentiation; 1 to the power of 850 and 9 minus 8 are both 1.

• good answer, even if there is too much space between the 1 and its exponent! – mau Mar 27 '17 at 20:51

I think I have it...

Change the 6 and 9 on the right to a 9 and a 6 (one step each, two total). Then take the minus sign between the 9 and 6, and move it to the 5 to create a 9. Now rotate it 180 degrees (aka look upside-down). You get 69-068=1.

• Instead of rotating 180 degrees (which requires all match sticks to be moved) you could say "look at it upside down". – Trenin Mar 27 '17 at 17:49
• rotating the view is a clever idea, but having a number starting with 0 is not, at least in my opinion... – mau Mar 27 '17 at 18:12
• @mau Numbers starting with 0 are valid, as long as you didn't specify they weren't. – Feathercrown Mar 28 '17 at 11:37

Step 1:

Move the bottom right match of the 6 to form a plus sign: 1=850-9+E

Step 2:

Move the top left match of the "E" to form a 2: 1=850-9+2

Step 3:

Move the bottom right match of the 5 to form an "E": 1=8E0-9+2

In which

E resembles the scientific notation "times 10 to the power of ___"

The idea is based on

kamenf's answer in the linked question, so credit to him/her as well.

• exponentiation was part of my own solution, but since this is not a display I am not sure E is allowed. (Then again, there is not an official solution, of course) – mau Mar 28 '17 at 9:05
• @mau You didn't say it wasn't allowed, so it's allowed. – Feathercrown Mar 28 '17 at 11:38

My attempt:

1 = 0009-8
Here are the steps:

Move the middle stick from the 8 and change the 5 to a 6
Move the middle stick from the 6 and change the 6 to a 0
Move the first subtraction to turn the 6 into a 8

If you

Look at it upside down

you will have

9-6-058=1

Now

Rotate the first minus sign by 45 degrees (1 movement). Then take a vertical stick on the left of the 8 and move it to convert this minus sign into a multiply sign (2 movements). Lastly, remove the other vertical stick on the left of the 8, which converts the 8 into a 3 (3 movements).

You will then have

9 X 6 - 053 = 1

Which is correct!!

NOTE: One match stick is removed completely, which isn't against the rules, but not be in the spirit of the puzzle.

• no match can be removed (or added). Otherwise it would be easy to obtain 1 = 0 + 9 - 8 – mau Mar 27 '17 at 18:15
• @mau how can you obtain that by moving only 3 match sticks? Note, I counted the removal of a match stick as a move. – Trenin Mar 28 '17 at 11:49
• @mau How about dropping the final stick ontop of he minus sign using two sticks for the minus? It isn't removing the stick, just putting it somewhere that doesn't change the equation. In fact, you can put it over any matchstick you want so long as it lines up correctly. – Trenin Mar 28 '17 at 11:55
• Raise something to the 1st power. – Random832 Mar 28 '17 at 18:07
• I agree with Random832, it's better to raise something to the first power – mau Mar 28 '17 at 18:10

This was a good little puzzle,

If multiplication is allowed 1 = 055 - 9 x 6, First use the middle of the 8 to make the x and a 0, then take 2 sticks from the 0, use one to make it into a 5 and then add the last stick to the 1 as a hat.

• But you need to keep one of those 2 sticks to turn the 0 into a 5 leaving you with only 1 stick to make into a hat or foot. – Trenin Mar 27 '17 at 17:59
• Also, your multiplication sign will be a little skewed. – Trenin Mar 27 '17 at 18:01
• Very true, in that case just add a hat to the 1, I will edit my answer – Gareth Shepherd Mar 27 '17 at 20:36
• Also I was not sure if the slight rotation of the one stick to match with the multiplication sign would count as a move or not, I assumed it would not – Gareth Shepherd Mar 27 '17 at 20:39

There were many nice solutions to the puzzle, and I have to decide which is the best one. Anyway, here there is my own:

Take the three bottom matches from the 0. Add one to the three remaining so to have a small zero as exponent; add another to the first minus to have another equal sign; add the last one to the 6, obtaining an 8. The final result is $1 = 85^0 = 9-8$ I wrote "an expression", not "an equation", so Scott has a point (but a single number is not "correct"), so that I can use two equal signs.

• To be fair, your own answer looks good to me. No weird spaces, no leading zeroes, no weird shapes as numbers or symbols. My answer, while a stretch (with the E operator), also fulfilled my own criteria :) – Pokemon Mar 29 '17 at 2:03

to change the 0 in 850 into a 6, change the 9 into an 8 by using the middle of the 8 in 856 and then turning the first minus sign by 45°, giving:

1=056/8-6

Taking advantage of arbitrary spacing and adding on far left and far right.

By the power of Javascript

Pick up the two matches making the = sign, and one of the two minus signs. Turn them into a 7 at the end of the statement.

So that evaluates to

18509-67

i.e.

18442

This works because

Anything is truthy, unless it is explicitly defined to be falsey. Falsey statements are false, 0, "", null, undefined, and NaN. 1+1=3 evaluates to false, but 2 is simply the integer 2. Non 0 integers are one example of a truthy value here.

You can move two matches from the 8 in 850 to the end of the 6, so that you have 61 and you are left with 550.

Not sure if you are allowed to alter any of the matches, but if you are, you can crumple up the - to form a dot, another way of representing x?

Which means you are left with 1 = 550 - 9 . 61

Otherwise, move the match at the bottom of the 9 to the minus and create a X?

1 = 550 - 9 x 61

• It seems you have two accounts now; you can use the contact us form to have them merged, so that you can edit your post instantly. – Glorfindel Mar 28 '17 at 13:26

Initial:

1 = 850 - 9 - 6

1st:

move a stick from the 8 to the 5 and you get
1 = 090 - 9 - 6

2nd:

1 = 090 - 9 - 6
move the right minus to the right 9 to make it an 8:
1 = 090 - 8 6

3rd:

1 = 090 - 8 6
move a stick in the 6 to make it a 9:
1 = 090 - 8 9

ok that way?